Adrien-Marie Legendre

Adrien -Marie Legendre [ ləʒɑ drə ː ] or [ ləʒɑ dʀ ː ] (* September 18, 1752 in Paris, † January 10, 1833 ) was a French mathematician.

Life

Legendre attended the Collège Mazarin, where he became in 1770 a PhD ( Thèse ). Since he was from a wealthy family, he lived thereafter until the French Revolution as a private scholar, and just out of interest he took from 1775 to 1780, by d' Alembert suggested an apprenticeship at the Paris Military Academy ( Ecole Militaire ) at. In 1782 he won the prize of the Berlin Academy of Science for determining the trajectory of a projectile with air resistance into account, which gave him the attention of Lagrange, who was director of the Academy in Berlin at that time. An application filed in January 1783 at the Paris Academy work on the attraction of ellipsoids, in which he also introduced the Legendre polynomials, gained him recognition in the leading French astronomer and mathematician Pierre Simon de Laplace, who made ​​sure that he and a corresponding member 1785 associate Member of the Academy of Sciences was. In 1785 he worked on elliptic integrals and 1786 with number theory - he formulated the Quadratic Reciprocity Law, the Leonhard Euler was already known.

In 1787 he was commissioned under Delambre and Méchain (another member was Cassini ) the longitude between Dunkirk and Barcelona - the longitude of the two places differ by only 13 arc minutes - measure geodetic triangulation, also with the aim of fundamentals for determining the Meters to win. They worked there together with the Observatory in Greenwich and also performed a triangulation of Greenwich to Paris. At that time he visited with Cassini also William Herschel in England and in 1787 a member of the Royal Society. The results reported Scripture exposé of operations, faites en France en 1787 (Paris, 1792). In 1791 he became a member of the Commission for the Reform of weights and measures ( metric Commission). From 1792, he was involved with Gaspard de Prony and other mathematicians such as Lazare Carnot in an extensive project to create mathematical tables ( tables of logarithms ).

During the French Revolution he lost his possessions and had to look for a job. In the time of terror, he even had to hide for some time. In 1793 he married Marguerite - Claudine Cohin. 1794 appeared the first edition of his textbook on geometry, which in the 19th century was very influential for the mathematics education not only in France, but also, for example, in the U.S. and many editions experienced. From 1795 he taught at the École normale supérieure. In 1808 he became a lifelong head of the University, appointed in 1815 Honorary Member of the Commission for public instruction and 1816 to the examiner at the École Polytechnique in place of Laplace. In 1812 he replaced Lagrange in the Bureau des Longitudes.

After he had fallen out with the government - he refused in 1824 to give a proposed their candidates for the Institute of France his approval - stressed he have his pension. He impoverished and died in 1833 in the Paris district of Auteuil.

Work

Legendre made ​​important contributions in various fields of mathematics, however, was made ​​as far back as those of 25 years younger Carl Friedrich Gauss in the shadow that in almost all areas worked in a remarkable parallelism over the same subjects as Legendre, but penetrated ever deeper. So Legendre discovered before Gauss 1806, the method of least squares, which he also used in astronomy (which, however, already Euler knew ( in the determination of comet orbits from three observations), and also found in front of Gauss the quadratic reciprocity law in works of 1751 and 1783 ) who collected first evidence of Gauss. The term Legendre symbol in number theory is a reminder of the achievements of Legendre in its formulation. Legendre recognized the contributions of Gauss and took it into account in the heavily revised second edition of his number theory from 1808, but at the same time complained bitterly that Gauss vice versa took all priorities lay claim. The asymptotic formula for the distribution of prime numbers is found in Legendre's number theory of 1798. She stands at the beginning of the use of analytical methods in number theory.

From the proof of Legendre (1825 ) of the Great Fermat's Last Theorem for the special case n = 5 is derived He also found in 1830 a new pair of amicable numbers, suspected the later proven by Dirichlet theorem that there are infinitely many primes in arithmetic progressions, where the first term is relatively prime to the difference of successive elements, and put on the Legendre conjecture that for is n> 0 and at least one prime between.

In calculus Legendre is known not only for its Legendre polynomials in the potential theory, but also for his work on elliptic integrals, in its division into three " classes " is named after him. He treated integrally along with other defined via integrals as functions of the gamma function and the beta function in his Exercises du calcul, which appeared in three volumes in 1811, 1817, 1819. In it, there are also applications of elliptic integrals and extensive tables. Later Legendre was no longer satisfied with the presentation and instead published a new edition of the three volumes of Traite des fonctions elliptiques (1825, 1826, 1830). At this time his book was already outdated by the pioneering work of Niels Henrik Abel and Carl Gustav Jacobi.

Of lasting influence was the geometry textbook by Legendre, in which he simplified the elements of Euclid and modernized first published in 1794. While still alive, it scored 15 runs, was translated into many languages ​​and was widely used in the 19th century at the schools, some in abbreviated form ( Blanchet, 1854, 1862). In the appendix, there are also simplifications of the proofs of the irrationality of ( first by Johann Heinrich Lambert proved) and of. In contrast to Gaussian he was convinced of the validity of Euclid's parallel postulate and tried for 30 years to prove futile. In 1787 he found the set of Legendre, an approximate formula for the approximation of spherical triangles.

In mechanics, Legendre is also known for the Legendre transformation.

Others

An engraving by Francois Seraphin Delpech - (1778-1825), which is often reproduced as a portrait of Legendre, not show it, but the politician Louis Legendre.

Legendre 's name immortalized on the Eiffel Tower, see: The 72 names on the Eiffel Tower.

The Moon crater Legendre is named after him.

Writings

  • Sur la figure of planetes. 1784th Here the Legendre polynomials are first mentioned.
  • Éléments de géométrie. Paris in 1794. This work is still often launched 1881 re-issued by Girard and 1858 by Crelle translated into German (Berlin).
  • Memoire sur les transcendantes elliptiques. Paris in 1794.
  • Essai sur la théorie of nombres. Paris 1797/1798. 2nd edition, two volumes; . Paris 1808 3rd edition 1830, two volumes; German Leipzig 1886.
  • Nouvelle théorie of parallel. Paris 1803.
  • Nouvelles methodes pour la determination of the Orbite comètes, etc. Paris, 1807. New Edition 1819, three volumes.
  • Exercises you calcul intégral. Paris 1811/1817, three volumes.
  • Traité des fonctions et elliptiques integral Euleriennes. Paris 1826-1829, three volumes.
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